please help to find the maximum and minimum of the objective function.

Hello, please help me to find the maximum and minimum of the following objective function (if they do exist) if there's no maximum state the reason.

f =3x+4y
then I'm given a graph with these points
(0,6)
(1,3)
(2,1)
(4,0)

thank you.

I would say the maximum is 24 at the points (0,6) however, that's wrong, according to my textbook, there's no maximum, why????
concerning the minimum, I agree with my textbook, the minimum is 10 at the points (2,1)
thank you.

Nov 22nd 2009, 12:57 AM

CaptainBlack

Quote:

Originally Posted by jhonwashington

Hello, please help me to find the maximum and minimum of the following objective function (if they do exist) if there's no maximum state the reason.

f =3x+4y
then I'm given a graph with these points
(0,6)
(1,3)
(2,1)
(4,0)

thank you.

I would say the maximum is 24 at the points (0,6) however, that's wrong, according to my textbook, there's no maximum, why????
concerning the minimum, I agree with my textbook, the minimum is 10 at the points (2,1)
thank you.

Please post the question as asked.

CB

Nov 22nd 2009, 04:18 AM

HallsofIvy

As Captain Black said, please post the entire problem. I can guess that you find max and min values in some convex set with vertices at those points (including the condition, that you did not state, that neither x nor y can be negative). If that is the case, then your text is right- there is no maximum because you can take x and y as large as you please. Note that the convex set having those vertices is unbounded. The region between those edges and the origin is concave, not convex. In any case, what was the problem, really?

Nov 22nd 2009, 08:34 AM

jhonwashington

Hello, this is what I'm asked:
In the following problem, use the given feasible region determined by the constraint inequalities to find the maximum of the given objective function (if they exist)
then I'm given the function : f=3x+4y
and then I'm given a graph which contains the following points:

(0,6)
(1,3)
(2,1)
(4,0)

thank you.

Nov 22nd 2009, 09:49 AM

HallsofIvy

Quote:

Originally Posted by jhonwashington

Hello, this is what I'm asked:
In the following problem, use the given feasible region determined by the constraint inequalities to find the maximum of the given objective function (if they exist)
then I'm given the function : f=3x+4y
and then I'm given a graph which contains the following points:

(0,6)
(1,3)
(2,1)
(4,0)

thank you.

And you still haven't stated the actual problem! You said "use the given feasible region determined by the constraint inequalities" but you have not stated any constraint inequalities! I can guess that the line, say, from (0,6) to (1,3), which is given by the equation y= -3x+ 6, forms part of the boundary of the feasible region, but without an inequality like or there is no way to tell which side of that line the feasible region is on!